Understanding the Recursion of mergesort

Question

Most of the mergesort implementations I see are similar to this. intro to algorithms book along with online implentations I search for. My recursion chops don\'t go much fur

Answer 1

My apologies if this has been answered this way. I acknowledge that this is just a sketch, rather than a deep explanation.

While it is not obvious to see how the actual code maps to the recursion, I was able to understand the recursion in a general sense this way.

Take a the example unsorted set {2,9,7,5} as input. The merge_sort algorithm is denoted by "ms" for brevity below. Then we can sketch the operation as:

step 1: ms( ms( ms(2),ms(9) ), ms( ms(7),ms(5) ) )

step 2: ms( ms({2},{9}), ms({7},{5}) )

step 3: ms( {2,9}, {5,7} )

step 4: {2,5,7,9}

It is important to note that merge_sort of a singlet (like {2}) is simply the singlet (ms(2) = {2}), so that at the deepest level of recursion we get our first answer. The remaining answers then tumble like dominoes as the interior recursions finish and are merged together.

Part of the genius of the algorithm is the way it builds the recursive formula of step 1 automatically through its construction. What helped me was the exercise of thinking how to turn step 1 above from a static formula to a general recursion.